Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913097813327872 |
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| author | Testa, Andrea Hauberg, Søren Asfour, Tamim Rozo, Leonel |
| author_facet | Testa, Andrea Hauberg, Søren Asfour, Tamim Rozo, Leonel |
| contents | The Schrödinger Bridge provides a principled framework for modeling stochastic processes between distributions; however, existing methods are limited by energy-conservation assumptions, which constrains the bridge's shape preventing it from model varying-energy phenomena. To overcome this, we introduce the non-conservative generalized Schrödinger bridge (NCGSB), a novel, energy-varying reformulation based on contact Hamiltonian mechanics. By allowing energy to change over time, the NCGSB provides a broader class of real-world stochastic processes, capturing richer and more faithful intermediate dynamics. By parameterizing the Wasserstein manifold, we lift the bridge problem to a tractable geodesic computation in a finite-dimensional space. Unlike computationally expensive iterative solutions, our contact Wasserstein geodesic (CWG) is naturally implemented via a ResNet architecture and relies on a non-iterative solver with near-linear complexity. Furthermore, CWG supports guided generation by modulating a task-specific distance metric. We validate our framework on tasks including manifold navigation, molecular dynamics predictions, and image generation, demonstrating its practical benefits and versatility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06856 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges Testa, Andrea Hauberg, Søren Asfour, Tamim Rozo, Leonel Machine Learning Differential Geometry 37K25 (Primary) 53D25, 49Q22 (Secondary) The Schrödinger Bridge provides a principled framework for modeling stochastic processes between distributions; however, existing methods are limited by energy-conservation assumptions, which constrains the bridge's shape preventing it from model varying-energy phenomena. To overcome this, we introduce the non-conservative generalized Schrödinger bridge (NCGSB), a novel, energy-varying reformulation based on contact Hamiltonian mechanics. By allowing energy to change over time, the NCGSB provides a broader class of real-world stochastic processes, capturing richer and more faithful intermediate dynamics. By parameterizing the Wasserstein manifold, we lift the bridge problem to a tractable geodesic computation in a finite-dimensional space. Unlike computationally expensive iterative solutions, our contact Wasserstein geodesic (CWG) is naturally implemented via a ResNet architecture and relies on a non-iterative solver with near-linear complexity. Furthermore, CWG supports guided generation by modulating a task-specific distance metric. We validate our framework on tasks including manifold navigation, molecular dynamics predictions, and image generation, demonstrating its practical benefits and versatility. |
| title | Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges |
| topic | Machine Learning Differential Geometry 37K25 (Primary) 53D25, 49Q22 (Secondary) |
| url | https://arxiv.org/abs/2511.06856 |